Method for simulating wave propagation; simulator, computer program and recording medium for implementing the method

ABSTRACT

Simulator, computer program and recording medium for implementing the method.

The invention relates to a method for simulating wave propagation,especially electromagnetic or even acoustic.

There is a growing need to use simulation, whether this is fordevelopment of novel products, or for qualification or homologation ofthe latter. In fact in the event where a product interacts with waves,it can be necessary to simulate propagation of these waves and theirinteraction with the product. The waves can in some cases be produced bythe product itself: this is the case for example for ultrasound sensors,radars or lidars.

This case therefore occurs especially during development of radars orlidars on board vehicles. Such sensors are increasingly provided onboard vehicles to ensure detection of obstacles and contribute toperforming functions of active safety, assistance in driving or evenautomatic driving.

PRIOR ART

With respect to simulation of radars, for real-time or semi-real-timeapplications, existing simulation methods are usually based on startingthem from a small number of rays, in a limited number of directions anda restricted solid angle, the objects present in the scene beingconsidered simplified in the form of their Radar Cross Sections (RCS).

Also, statistic models originating from a test campaign are sometimesalso used for simulation of radars.

If the use of RCS tables is often acceptable for aerial radars, forwhich the number of objects to be modelled is very restricted, inverselythis method is inapplicable for radars on board terrestrial vehicles,whereof the close environment comprises a very wide variety of possibleobjects, and also moveable relative to each other.

In fact in such environments, propagation simulation of radar wavesbased on RCS tables, in practice proves insufficient since it managesonly relatively approximately the masking of elements and dephasingcaused by multiple rebounds before the wave returns to the antenna.

The method therefore does not simulate waves received in returnsufficiently closely to reality.

PRESENTATION OF THE INVENTION

As a result, there is a need for a method for simulating wavepropagation, especially of electromagnetic waves (in particular, wavesoutside the visible spectrum, and/or non-coherent waves) or acousticwaves, which is likely to provide a representation of the propagation ofsimulated waves more realistically than simulations performed by usingRCS.

This aim is achieved because the method comprises the following steps:

a) scene data are provided representing a three-dimensional scenecomprising at least one object having a plurality of surfaces, each ofsaid surfaces having a normal;

b) a plurality of primary rays emitted in respective propagationdirections is calculated by means of a computer, each of said primaryrays being defined at least by a transported power, a position, and adirection of propagation;

d) as a function of a point of reception, primary diffused rays arecalculated by means of a computer, each of said primary diffused raysbeing emitted by a surface of said at least one object of the scenereached by a primary ray.

A ray diffused by a surface reached by a ray, so-called incident ray,here designates a ray emitted by the reached surface under the effect ofthe incident ray, having a direction of propagation passing through thepoint of reception, and having a transported power at least function ofa relative orientation between the direction of propagation of theincident ray and the normal to the reached surface.

As the direction of propagation of a diffused ray, by definition, passesvia the point of reception, a diffused ray is therefore (with someexceptions) a ray which is emitted in a direction other than thedirection of a specular ray (ray reflected by the surface by specularreflection of the incident ray). In particular, the point of emissionfrom which the primary rays are emitted is almost always very close tothe point of reception; as a result, it is impossible for a specular rayto be directed to the point of reception.

Also in general, under the effect of the incident ray the surfacetherefore on the one hand emits a diffused ray and on the other handemits different re-emitted rays, having propagation directions notpassing through the point of reception (one of them being the specularray).

The term ‘calculation of a ray’ here designates calculation of theattributes or characteristic parameters of this ray.

The “position” of a ray can be especially any information defining thepoint of emission of this ray. It can be obtained by means of theattributes of the point of emission of the ray.

The simulation method therefore determines the different rays receivedby an observer placed at a given point relative to the scene, so-calledpoint of reception.

As is known per se, the method uses the technique of the “ray tracing”:the wave emitted is considered as being the meeting of a set of emittedrays here called “primary rays”.

An important characteristic of the method is the fact that during stepd) rays diffused by the surfaces of the objects present in the scene arecalculated.

For these rays, the transported power is at least a function of therelative orientation between the direction of propagation of theincident ray and the normal to the reached surface (This relativeorientation is called hereinbelow “incidence angle” of the ray on thereached surface). So step d) simulates the radiation seen in return bythe observer placed at the point of reception by taking into account thegeometry of objects present in the scene, this geometry being taken intoaccount by the fact that for each diffused ray the power transported bythe diffused ray depends on the incidence angle of the primary ray onthe reached surface.

The radiation seen in return at the point of reception is thesuperposition or the sum of diffused rays by the different surfaces ofthe objects of the scene in the direction of this point.

Modelling Objects

In general, objects present in the scene are recorded in the form of aset of planar surfaces: the normal to the surface of the object reachedby the incident ray is simply the normal of the planar surface reachedby the incident ray. Planar areas can be planar facets, especiallytriangular.

Other types of modelling of the geometry of the objects present in thescene can especially be envisaged, especially by non-planar surfaces(for example defined by B-splines, Bezier curves, etc.).

Modelling of the Rays; Ray/Surface Interaction

The quality of the simulation performed further depends on the modelused for the interaction between the incident ray and the surfacereached by the latter.

The predetermined interaction model between an incident ray and asurface of an object defines the properties of the ray(s) optionallyemitted by the surface, as a function of the properties on the one handof the incident ray that reaches the surface, and on the other hand ofthe surface.

The ray(s) emitted by the surface are (exclusively) either diffused rayssuch as defined previously, or rays known as “re-emitted” rays.

The calculation of the ray(s) emitted comprises the calculation ofdifferent parameters.

These parameters can include especially, for the emitted ray: itsdirection of propagation; its point of emission (this is the point ofthe surface reached by the incident ray); the energy or the powertransported by the emitted ray; the polarisation of the emitted ray; thephase of the signal brought by the emitted ray; the distance covered bythe ray from emission of the primary ray of origin; the frequency of thesignal brought by the emitted ray.

They can also optionally comprise characteristics of transverse form ofthe ray, that is, characteristics of the form of a section of the ray ina plane transverse to its direction of propagation.

The values of each of the parameters of the ray can vary as a functionon the one hand of the trajectory between the point of emission of theincident ray and the reached point on the reached surface (especiallyoptionally as a function of parameters of the atmosphere between thesetwo points); and on the other hand as a function of properties of thesurface reached by the incident ray.

In particular, the energy or the power transported by a diffused orre-emitted ray can be at least a function of relative orientationbetween the incident ray and the normal to the surface reached by thelatter.

The properties of a diffused or re-emitted ray, especially the energy orthe transported power, can also optionally depend on the angle betweenthe direction of propagation of this ray and the normal direction (orperpendicular) to the surface at the point of emission of this ray.

Also, the properties of diffused or re-emitted rays can depend, not onlyon the positions or relative orientations of the incident ray relativeto the reached surface of the object, but also on properties of theobject itself.

In an embodiment, a property, especially physical, of materialconstituting a surface of an object of the scene is used for calculatingthe diffused rays.

The property in question here can be a coefficient of reflection ortransmission of the material of the reached surface of the object.

For example, the property of the surface can especially be defined bycoefficients of reflection, transmission, scattering, of the incidentray, or by the electrical and magnetic permeabilities of the material inquestion, which can be single real numbers. The property of the surfacecan also be defined as much more complex for example by being a functionof the bidirectional reflectance distribution function, or BDRF, of thematerial of the surface in question.

In this embodiment, it therefore suffices to attribute some parameters,some properties to materials, and to then define that surfaces ofobjects present in the scene consist of the material(s) as defined.

For calculation of a diffused ray, a predetermined interaction modelbetween an incident ray and a surface reached by the latter can beconsidered.

So for example, in an embodiment, and in the event where the waves areelectromagnetic, at step d) the power or the energy transported by thediffused ray(s) is calculated by using the electric field integralequation (EFIE). Advantageously, this equation calculates the propertiesof the diffused rays relatively simply.

Steps a), b) and d) of the simulation method described previouslyeffectively simulate the propagation of rays in a three-dimensionalscene.

However, the simulation method can be made even more realistic by takinginto account the multiple reflections of the rays striking the scene.

With this aim, in one embodiment the simulation method further comprisesa complementary step c) during which:

c) the propagation of incident rays is simulated especially iterativelysuch that at each iteration for each incident ray in question:

-   it is determined if the incident ray, by propagation in a straight    line, reaches a surface of an object of the scene; and-   if as a function of a predetermined interaction model between an    incident ray and a surface of an object at least one re-emitted ray    (ray emitted by a surface of the scene, other than a diffused ray)    is emitted after interaction of said incident ray with said reached    surface:    -   the point reached on the reached surface is determined; and,    -   said at least one ray re-emitted from the reached surface is        calculated; said incident rays in question being:-   during the first iteration, the primary rays calculated at step b);-   during each of the subsequent iterations, the re-emitted rays    calculated at the preceding iteration.

Furthermore at step d), the diffused rays emitted by the surfaces of theobject(s) of the scene reached by a re-emitted ray are also calculated.

In this embodiment, the method can comprise one or more iterations atstep c).

Also, as for the diffused rays a property, especially physical, ofmaterial constituting a surface of an object of the scene can be usedfor calculating the re-emitted rays.

The re-emitted rays such as defined at step c) can correspond to atransmitted wave or to a wave reflected by the object whereof thesurface is reached by the incident ray. Other types of re-emitted rayscan be taken into consideration as a function of the nature of the waveswhereof propagation is simulated.

At step c), determining the reached point on the reached surface canconsist of determining a point, defined by three-dimensionalcoordinates, or even by bidimensional coordinates on the reachedsurface. But that can also consist more widely of determining thereached surface, or part of the reached surface, therefore thisoperation is sufficiently precise to enable calculation of thecharacteristics of rays emitted following interaction of the incidentray with the reached element (reached point, portion of surface, orsurface).

So in this embodiment of the method according to the invention, the ‘raytracing’ technique is carried out much more realistically than in formerembodiments wherein interaction between an object and an incident raywas modelled in a very simplified way by means of RCS.

In fact at step c) calculation of the re-emitted rays produces a moreprecise representation of the propagation of waves.

The re-emitted rays are generally calculated by taking into account thegeometry of the object(s) present in the scene. So for example, one ormore properties of the re-emitted ray(s) can be a function of the normalof the reached surface. The normal of the reached surface of the objectis calculated naturally at the point of the surface reached by theincident ray.

In the event where the waves are electromagnetic waves the interactionmodel between the incident ray and the surface can be founded on theequations of physical optics.

In this case, in an embodiment, the power transported by a re-emittedray is calculated by the Snell-Descartes law.

To calculate the direction of propagation of the re-emitted ray(s), inone embodiment, the direction of propagation of at least one emittedray—and in general, of each of the re-emitted rays—depends solely on thedirection of propagation of the incident ray and of the normal of thereached surface.

Via following step c), and in the event where the rays areelectromagnetic in nature, for each incident ray only zero or a rayreflected by the surface (specular reflection) and optionally a raytransmitted inside the surface is calculated, if the surface istransparent. Following step d), if there is cause, the diffused ray iscalculated by the surface under the effect of the incident ray.

Also, the method according to the invention, advantageously is a methodhaving substantially constant complexity; i.e, the number of raysgenerally is relatively constant throughout the iterations.

In fact the incident rays which encounter no surface do not produce anyemitted ray; inversely, transparent surfaces (which generally form onlya minimal proportion of surfaces) can produce two re-emitted rays forone incident ray.

To determine the frequency of an emitted ray calculated at step c), inan embodiment, a relative speed of the surface reached by the incidentray, relative to the point of reception, is considered (it is a relativespeed because the point of reception itself can optionally be animatedby its own speed).

Structure of Data; Calculation Means: GPU

In addition to the physical parameters which govern the propagation ofstudied rays, the choice of some specific calculation means implementsthe method particularly efficaciously.

In particular, due especially to the choice of algorithm of ray tracingfor the propagation of the emitted wave, the method can advantageouslybe implemented on a graphics card. So in a particularly interestingembodiment of the invention, step c) and/or step d) is conducted on a(single) graphics card (CGU), and the calculations made for each of therays are done in parallel.

This embodiment therefore performs calculations of step c) and/or d)particularly rapidly. Because of this, the method can advantageously beimplemented in real time or semi real time.

To implement the method on a graphics card as indicated previously, thescene data preferably consist mainly of at least one multidimensionalmatrix, or else by a set of individual three-dimensional data.

In the first case, the geometry of the objects is not recorded in theform of three-dimensional coordinates. On the contrary, the position ofthe objects is recorded in the form of the coordinates (line number andcolumn number) of a datum in a matrix, as well as in the form of a depthvalue usually called ‘z’. The geometry is therefore stored in one ormore matrices usually called «Z-buffer». This matrix or these matricescontaining geometry information of the objects of the scene form part ofthe scene data, recorded in a multi-dimensional matrix called ‘G-buffer’(buffer or graphic buffer).

“Multi-dimensional” matrix here designates a set of matrices having thesame number of lines and columns. Advantageously, a multi-dimensionalmatrix stores, for a same position (i,j) in the multi-dimensionalmatrix, not only scale information (such as for example depthinformation ‘z’), but any amount of information relative to the elementreferenced at the placement (i,j).

In the second case by way of contrast, the geometry is recorded in theform of three-dimensional data. In this case, the scene data mainlycomprise entities which contain the three-dimensional coordinates of thedifferent surfaces of the objects contained in the scene. They canfurther comprise other data, recorded for example in multi-dimensionalmatrices, especially the different coefficients characterising thesurfaces of the objects of the scene.

Furthermore, just as the scene can be recorded in a multi-dimensionalmatrix, the rays (primary, and/or diffused, and/or re-emitted) canadvantageously also be recorded. Therefore in an embodiment, the primaryrays, the re-emitted rays, and/or the diffused rays are recorded in amultidimensional matrix.

Preferably at step c) the direction of propagation of the re-emittedrays is calculated by means of the scene data and the characteristics ofthe incident rays, without introducing other data representing thegeometry of the scene.

Also, in an embodiment of the method according to the invention, thecalculations required at step c) and/or d) can be programmed onmultiprocessor graphics card by means of “shaders”.

A shader is a program, written in a language—either assembler or ahighest-level language—directly executable by a graphics processingUnit, “GPU”, and which replaces some parts of the usual executionpipeline. It is possible especially to use shaders programmed in GLSLlanguage (“openGL Shading Language”).

The use of “shaders” absolutely requires recording or modelling the dataor information in the form of multidimensional matrices, which processesthem by “shaders” substantially parallel, in a space called “imagespace”.

This programming mode is therefore particularly adapted to the casewhere the scene and/or the rays (primary, re-emitted, and/or diffused)are represented by multidimensional matrices (i.e, by a G-buffer such aspresented earlier).

In another embodiment, the calculations required at step c) and/or d)can be programmed on multiprocessor graphics card by using a programminglanguage for multiprocessor graphics card authorising direct access toinstructions and the memory of the different parallel calculationprocessors of the graphics card, such as for example the Cudaprogramming language (registered trade mark).

This mode of programming can especially be selected when the scene isrepresented in the form of three-dimensional data.

Simulation of Sensors

A particularly important application of the method for simulating wavepropagation according to the invention is the simulation of sensors.

The invention also relates to a method for simulating a sensor,especially a sensor for a motor vehicle, the sensor being provided toemit waves and produce an output signal as a function of waves receivedin return following said emission of waves, the method comprising thefollowing steps:

i) the emission of waves is simulated by the sensor, and the propagationof said waves, so as to determine rays received by the sensor, bycarrying out a method for simulating wave propagation such as definedpreviously; and

ii) the output signal of the sensor is determined as a function of therays received by the sensor and predetermined characteristics of thesensor.

Sensor simulation is therefore first done by simulating the emission ofwaves by the sensor, then their propagation (step i). During propagationsimulation of waves at this step i), the propagation of waves issimulated so as to calculate the diffused rays to be received by thesensor placed at the point of reception.

As a function of the characteristics of the sensor, the output signal ofthe sensor is then calculated. This calculation can be performed indifferent ways.

In an embodiment, the output signal of the sensor is determined at stepii) by performing the following two steps e) and f):

e) the respective signals of at least one part of said diffused rays arecalculated; and

f) a signal received at the point of reception is calculated by addingthe respective signals calculated at step e2).

The output signal of the sensor is determined as a function of thesignals from the different diffused rays returned by the scene andreceived by the sensor at the point of reception.

In particular, to limit calculation time it is preferable to calculatethe signals transported by the diffused rays only for a reduced numberof diffused rays.

For this purpose, step e) preferably comprises the following twosub-steps:

e1) a sub-set of diffused rays is selected as a function of apredetermined criterion, especially a criterion taking into account thetransported power of the diffused rays, and/or at least onecharacteristic of adjacent rays such as total covered distance and/or aphase of the transported signal;e2) the respective signals of the selected diffused rays are calculatedonly for the selected sub-set of diffused rays.

Typically, at step e) the selection of the sub-set of diffused rays isdone by sorting the diffused rays by order of power or transportedenergy.

However, the respective signals from the different diffused rays canoptionally be calculated for all the diffused rays.

The addition of the respective signals of the different diffused raystakes into account the respective characteristics of the diffused raysso as to produce an accumulated signal representative of reality.

Different parameters can be considered for boosting the quality of thesimulation.

In an embodiment, for each re-emitted ray calculated at step c) adistance covered by the ray from the point of emission of the primaryray having generated the re-emitted ray in question is determined.

At step f) especially, this calculates for each selected diffused raythe power of the signal received by the sensor, taking into account thetotal distance effectively covered by the diffused ray, and consequentlythe loss of power (expressed for example in dB) which ensues.

The quality of the simulation can further be improved by adding a noiseto the respective signals of the different selected diffused rays,and/or to the received signal calculated in this way.

The quality of the simulation can also be improved by taking intoaccount precisely the operation of the wave emission antenna of thesensor (the term ‘antenna’ is used here to designate any wave emissionsystem included in the sensor).

In an embodiment, at step b) an emission diagram is provided indicatingpower losses as a function of the direction of propagation, and thepower transported by the primary rays is calculated as a function of theemission diagram.

The emission diagram realistically takes into account the real emissionproperties of the antenna of the sensor.

The invention also relates to a method for simulating a motor vehiclecomprising at least one sensor, wherein a propagation of waves emittedand/or received by the sensor is simulated by carrying out a method forsimulating wave propagation such as defined previously, in particular amethod wherein the sensor is simulated by the sensor simulation methodsuch as defined previously.

The invention also relates to a computer program comprising instructionsfor execution of the steps of one of the simulation methods definedpreviously.

The invention also relates to a recording medium readable by a computeron which a computer program is recorded comprising instructions forexecution of the steps of one of the simulation methods definedpreviously.

The invention finally also relates to a wave propagation simulator,comprising:

a) a memory, capable of storing scene data representing athree-dimensional scene including at least one object having a pluralityof surfaces, each of said surfaces having a normal;

b) primary calculation means, capable of calculating a plurality ofprimary rays emitted in respective propagation directions, each of saidprimary rays being defined at least by a transported power, a position,and a direction of propagation;

d) calculation means for diffused rays, capable of calculating as afunction of a point of reception of the primary diffused rays, each ofsaid primary diffused rays being emitted by a surface of said at leastone object of the scene reached by a primary ray;a ray diffused by a surface reached by a ray, so-called incident ray,being a ray reflected by the reached surface under the effect of theincident ray, having a direction of propagation passing through thepoint of reception, and having a transported power at least function ofrelative orientation between the incident ray and the normal to thereached surface.

In an embodiment, this simulator further comprises:

c) calculation means for re-emitted rays capable, especiallyiteratively, at each iteration and for each incident ray in question:

of determining if the incident ray, by propagation in a straight line,reaches a surface of an object of the scene; and

-   if as a function of a predetermined interaction model between an    incident ray and a surface of an object, at least one re-emitted ray    is emitted after interaction of said incident ray with said reached    surface:    -   of determining the reached point on the reached surface; and    -   of calculating said at least one re-emitted ray from the reached        surface;        said calculation means for re-emitted rays being arranged so as        to take into consideration as incident rays:-   during the first iteration, the primary rays calculated at step b);-   during each of the subsequent iterations, the re-emitted rays    calculated at the preceding iteration.

Furthermore, the calculation means for diffused rays are capable, atstep d), of calculating diffused rays emitted by the surfaces of said atleast one object of the scene reached by a re-emitted ray.

The invention will be understood and its advantages will emerge moreclearly from the detailed following description of embodimentsillustrated by way of non-limiting examples. The description refers tothe appended drawings, wherein:

FIG. 1 is a schematic view of a road on which three vehicles travel;

FIG. 2 is a schematic view representing a data structure for recordinggeometry of a scene;

FIG. 3 is a schematic view representing the interaction of an incidentray with a surface of an object;

FIG. 4 is a schematic plan view representing the propagation of primaryrays projected by the radar in the scene of FIG. 1;

FIG. 5 is a schematic plan view representing the propagation ofre-emitted rays emitted by the vehicles present in the scene of FIG. 1after reception of the primary rays;

FIG. 6 is a schematic plan view representing the propagation of diffusedrays by the vehicles present in the scene of FIG. 1 after reception ofthe primary rays;

FIG. 7 is a schematic view of a signal transported by a radar ray;

FIG. 8 is a schematic view of a signal received by the radar; and

FIG. 9 is a schematic representation of the method for simulating wavepropagation according to the invention.

An embodiment of the method and of the device according to the inventionwill now be described in reference to the figures.

In the embodiment presented, the wave propagation method is apropagation method of electromagnetic waves used to simulate theoperation of radar on board a vehicle, for example a car.

Such radar is implemented typically in a scene such as that shown inFIG. 1.

This figure illustrates three cars A, B, C travelling on a road 10. Thecar C is equipped with a radar 12 and emits from a point P (moreprecisely, from an area considered as substantially specific)electromagnetic radiation.

The portion of this radiation which is exploited is that whichpropagates in the solid angle S shown in FIG. 1. This solid angle Sdivides itself into a matrix of elementary solid angles S_(ij) where idesignates the line and varies from 1 to n, and j designates the columnand varies from 1 to p.

The part of the space included in the solid angle S, and limited to theside in front of the car C by a plane L located at a predetermineddistance from the car C (actually around 200 meters from the latter)constitutes a scene 14. The function of the radar 12 is to detectobstacles inside this scene.

In a first instance, the major steps of method for simulatingpropagation of rays according to the invention will be presented inrelation to FIG. 9.

This figure presents the radar simulation as a peripheral process of aprincipal process which is the operation simulation of a motor vehicle.

The car C travelling on the road 10 in fact is simulated by a motorvehicle simulator 100.

This simulator 100 includes a central calculator 102 which executes acomputer program 104 for vehicle simulation, so-called ‘simulationmotor’. This program 104 simulates the travel of a vehicle, andespecially in the present case, the travel or displacement of the car C.

For this, the program 104 simulates the acquisition of differentinformation acquired by the sensors of the car C. It therefore simulatesespecially the acquisition of information supplied by the radar 12.

This latter simulation (radar simulation) is performed by a radarcomputer 110 which comprises a central unit 112 with a main processorand a storage memory, as well as a graphics card 114.

The program 104 operates iteratively, with a processing loop in realtime or in semi-real time simulating the evolution of the traffic atregular intervals, for example 40 ms (in real time).

At each processing loop, the program 104 transmits to the radar computer110 the geometric description (‘G’, FIG. 9) of the scene which is facingthe radar 12 at the relevant instant. This description includes therelative speeds relative to the radar 12 of the different objectspresent in the scene.

In the graphics card, a processing program also noted 114 is recorded.

The graphics card executes the program 114 so as to perform thefollowing processing:

a) On receipt of data relative to the scene 14, the program 114constitutes scene data representing the scene placed facing the radar12;

b) the program 114 realises a ‘ray tracing’, and thus calculates thecharacteristics of the different primary rays which are emitted by theradar;

c) iteratively, the program 114 simulates the propagation of theincident rays in the scene 14. These incident rays are:

-   during the first iteration, the primary rays emitted by the radar;    and-   during each of the subsequent iterations, the re-emitted rays    calculated at the preceding iteration.

Also, at each iteration and for each of the incident rays, the program114 determines if the incident ray reaches a surface of an object of thescene by propagation in a straight line.

If this is the case, the program 114 determines whether one or more raysare re-emitted after interaction of the incident ray in question withthe reached surface. Emission of one or more rays after thisinteraction, and the characteristics of the re-emitted ray(s), aredetermined as a function of the interaction model between an incidentray and a surface of an object, which is chosen in advance.

The program 114 therefore on the one hand determines the reached pointon the reached surface; and on the other hand the characteristics of there-emitted ray(s) from the reached surface under the effect of theincident ray in question.

d) the program 114 calculates the rays diffused by the differentsurfaces present in the scene 14 in the direction of the point ofreception, i.e, here in the direction of the radar 12;

e1) the program 114 selects a sub-set of diffused rays as a function ofa predetermined criterion taking into account the power or thetransported energy of the diffused rays; it transmits this informationto the central unit 112 of the computer 110.

In the central unit, a processing program also noted 112 is recorded.The program 112 executes the following processing:

e2) the program 112 calculates signals respectively for each of theselected diffused rays at step e1).

f) the program 112 calculates a signal received by the radar by addingthe respective signals calculated at step e2). It calculates the outputsignal Sr of the radar as a function of the signal received by theradar.

a) Scene Data

To simulate the operation of the radar 12, scene data representing thescene 14 are used or are first created.

These data comprise at a minimum a set of geometric data including inprinciple any object present in the scene, on condition that the latteris of sufficient size to be detectable in a solid elementary angleS_(ij).

For each object, the scene data therefore comprise, for its differentsurfaces likely to be illuminated by a ray emitted by the radar, asimplified description of the surface, comprising especially thecoordinates of the normal vector to the surface.

The scene data also preferably include different coefficients orparameters characterising the surface (or of the material constitutingthe surface) and serving as calculation of the re-emitted rays followinginteraction of an incident ray with the surface.

These coefficients can be especially coefficients characterising theproperties of the surface relative to reflection, transmission andscattering of incident rays.

These coefficients can be for example refractive indices, thickness,roughness . . . .

Furthermore, the scene data can include, for each surface, indication ofthe instantaneous speed of the surface relative to the radar.

These different coefficients are in general recorded by reference to thematerial constituting the surface.

In this case, for each material constituting a surface of the objectspresent in the scene 14, coefficients characterising the response of thematerial are recorded when a surface consists of this material receivesan incident ray, this incident ray having the frequency and the waveform produced by the radar whereof the operation is simulated.

The scene data are recorded in the memory of the graphics card 114.

They can be recorded in different ways.

In the embodiment presented here, they are recorded in the form of amultidimensional matrix M (FIG. 2), also called “G-buffer” or“Graphics-buffer”. The matrix M includes the same number of lines andcolumns as the matrix of elementary solid angles, but it consists of acertain number (q) of individual matrices, noted M₁, M₂, . . . M_(q). Inthis way, the location of each surface of an object of the scene isrecorded only on the one hand via the components (i,j) of the matrixelement wherein the surface is recorded, and on the other hand by adepth information ‘z’, which is recorded in the matrix M, for example inthe matrix M₁. This is therefore a Z-buffer.

The following matrices M₂, M₃, . . . M_(u) serve to record the otherproperties of the surface (these properties are recorded in this exampleby u−1 real numbers). These other properties can consist of anindication of the material constituting the surface, the properties ofthis material also being recorded.

If in a given elementary solid angle, the scene comprises severalsuccessive surfaces at increasing distances of the point P, thesedifferent surfaces are recorded in the matrix M, in individual matricesM_(k), where k begins for example at the value u+1.

Alternatively, the scene data can be recorded as a three-dimensionalscene comprising objects in turn composed from a set of facets,especially triangular, surface properties being associated with thefacets in the form of textures especially, by means of texturecoordinates as is known per se.

b) Calculation of Primary Rays

The simulation of the operation of the radar first requires calculationof the rays emitted by the radar from the point of emission P (primaryrays).

To simplify calculation, a primary ray P_(ij) is calculated for eachelementary solid angle S_(ij). The primary rays are therefore recordedin a multidimensional matrix similar to the matrix M describedpreviously.

FIG. 4 illustrates in a schematic way the primary rays P_(ij) emitted ona horizontal line of solid angles S_(ij).

For each primary ray P_(ij) the following information is recorded:

-   -   its direction of propagation (this is recorded implicitly by the        coordinates (i,j) of the ray in question P_(ij));    -   its point of emission (for the primary rays, it is the point P);    -   the power transported by the emitted ray. This information is        recorded in the form of a gain—negative—in dB relative to the        maximal initial power of a primary ray;    -   the polarisation of the primary ray;    -   the phase of the signal carried by the primary ray;    -   the distance covered by the ray from the emission of the primary        ray of origin (zero distance, in the case of primary rays);    -   the frequency of the signal carried by the primary ray.    -   the Doppler coefficient linked to the primary ray (zero        coefficient in the case of primary rays).

The gain value is not the same for all primary rays. In fact, for eachprimary ray, the gain is provided by the emission diagram of theemission antenna of the radar 12. This antenna diagram indicates, as afunction of the elementary solid angle S_(ij), the energy or theeffective power- and therefore the gain—of the ray which the radar emitsin the elementary solid angle. It is therefore this value which isrecorded as initial gain for each primary ray. Actually, the gain ofprimary rays is high at the centre of the ray emitted by the radar, andweaker at the sides.

c) Propagation of Rays

The propagation of rays is founded on an interaction model with thesurface as known per se (FIG. 3). According to this model, as a functionof parameters of reflection, transmission and scattering of the surface,when an incident ray R_(i) strikes a surface at a point E, it can beabsorbed without emission of any radiation; it can produce a reflectedray Rr; it can produce a transmitted ray Rt.

The characteristics of these different rays each depend on the directionof incidence (and therefore on the direction of propagation of theincident ray) and on the normal n to the surface.

Also, radiation can be diffused from the point E in the direction ofreception (which can be the direction of emission of the primary rays);there is projection of a diffused ray Rd in the direction of the pointP.

Furthermore, in this embodiment, interaction of the incident ray withthe reached surface is based on the following hypotheses:

It is considered that the incident ray acts a planar monochromatic wave,and even if the signal transported by the incident ray (for example, inradars having FMCW, FSK modulations, having pulses, . . . ) is inreality the superposition of several monochromatic waves.

It is also considered that when an electromagnetic wave front interactswith the surface of an object (or the interface between two media), thissurface is considered locally as planar and it is assimilated as aninfinite plane for calculation of the emitted ray. (However, calculationcan optionally include the curve of the surface).

An example of an interaction of primary rays with the objects of thescene is illustrated by FIGS. 4 to 6.

In one of the emission planes of primary rays P_(ij) (j=Cte),illustrated by FIG. 4, the primary rays strike the vehicle A in threeelementary solid angles and the vehicle B also in three elementary solidangles (bold arrows, FIG. 4).

For each primary ray P_(ij), during the first iteration of the program114 at step c) the interaction of different primary rays P_(ij) with thesurfaces of the objects present in the scene is evaluated.

It is evident that interaction with the ground constituting the road 10must normally be taken into account; however for simplifyingexplanations, this interaction is not discussed in the example shown.

On vehicle A, the reached surfaces are opaque surfaces located behindthe vehicle; no ray is transmitted through the surface. But thesesurfaces do produce three re-emitted reflected rays R_(rA).

On vehicle B, the reached surfaces are the transparent surfaces of thefront windshield of the vehicle. These surfaces first produce threere-emitted reflected rays R_(rB). Being transparent, they also producethree re-emitted transmitted rays R_(tB).

The evaluation of the interaction between the primary rays (or, at latersteps of calculation, the incident rays) and the surfaces of the objectsof the scene therefore results in creating new rays, the re-emitted raysR_(rA), R_(rB), R_(tB).

These rays do not have the same characteristics as the primary rays.

Their characteristics are calculated as follows:

the direction of propagation is calculated as per the interaction modelwith the surface in question as a function of the direction of theincident ray and of the normal direction of the surface at the pointstruck by the incident ray;

the point of emission of the re-emitted ray is the point of the surfacestruck by the incident ray;

the gain, the polarisation of the re-emitted ray are calculated as perthe interaction model with the surface in question, as a function of thecharacteristics of the surface, and optionally as a function of thedirection of the incident ray and of the normal direction of the surfaceat the point struck by the incident ray;

the phase of the signal carried by the re-emitted ray, and the distancecovered by the ray from the emission of the primary ray of origin, arecalculated as a function of the position of the point struck on thesurface, relative to the radar, and optionally as a function ofproperties of the surface; and

the frequency of the signal carried by the re-emitted ray is calculatedas a function of the relative speed of the surface relative to theradar.

An important parameter is the gain of the re-emitted ray, whichcorresponds to the power of the signal transported by the ray.

The program 114 calculates the gain of the re-emitted rays by using theequation of physical optics: The power transported by a re-emitted rayis calculated by the Snell-Descartes law.

Naturally, a large number of primary rays encounters no surface of anobject of the scene 14; these rays do not produce any emitted ray.

At step c), after the first interaction of each of the primary rays withthe surfaces of the objects of the scene 14 has been evaluated, theprogram 114 can perform one or more iterations so as to calculate one ormore subsequent interactions between the re-emitted rays and thesurfaces of the objects of the scene.

In the example shown however, the program 114 is parameterised so as topass step d) as soon as the second iteration of step c) has beenperformed, i.e, as soon as all the primary rays have reached thesurfaces they can reach by propagation in a straight line from point P.

More generally, the program 114 can be parameterised so as to pass stepd) either after a fixed number of iterations, or when another criterionhas been attained.

Optionally, step c) can not be performed. The program 114 moves directlyfrom step b) to step d).

The calculations are performed substantially parallel on the graphicscard 114. The number of primary rays is selected so as to engender anumber of rays which can be processed by the graphics card at thepreferred processing frequency.

d) Calculation of Diffused Rays

At step d), the program 114 calculates the diffused rays by thedifferent surfaces present in the scene 14 in the direction of the radar12.

This calculation is done for each of the surfaces of the scene 14. Thesame surface can optionally produce several emitted (diffused orre-emitted) rays if it is reached by several incident rays, especiallyduring several iterations performed at propagation step c).

In the example shown, step c) is stopped on completion of the firstiteration.

The program 114 therefore calculates six diffused rays: three raysR_(dA) diffused by the rear wall of the car A, and three rays R_(dB)diffused by the front wall or the side wall of the car B. The program114 does not calculate ray R_(dB) for the other surfaces of the car B,since on completion of the first iteration (FIG. 5), only the front walland a side wall of the car B have been reached by incident rays (sincethis is the first iteration, the incident rays are the primary raysP_(ij)).

For each surface of the scene 14, the program 114 calculates anydiffused ray(s) emitted by the surface, taking into account the set ofincident rays having reached the relevant surface during the differentiterations of step c).

The diffused rays comprise substantially the same parameters as theprimary rays.

e1) Sorting and Selection of Diffused Rays

Following step e1), the program 114 selects a sub-set of diffused raysas a function of a predetermined criterion taking into account the powertransported by the diffused rays.

This criterion is founded more precisely on the power returned to theantenna, which is a function of the power transported by the diffusedrays.

The power returned to the antenna by a diffused ray is calculated on thebasis of characteristics of the reception antenna of the radar 12,especially the dimensions or the surface of the latter. It is optionallycalculated as a function of the gain of the antenna, this gain dependingon the direction of origin of the diffused ray.

More specifically, this power is calculated on the basis of the electricfield integral equation, by integrating the flow of the Poynting vectorof the diffused ray through the surface of the antenna.

The calculation for each diffused ray of the power returned to theantenna by the diffused ray proceeds with selection of the diffused rayswhich will be considered for calculation of the signal receivedeffectively by the radar. In fact, this selection actually consists ofthen considering calculating only those rays which will returnsubstantial power to the radar.

For this purpose, the first step is sorting the diffused rays as afunction of the power returned to the antenna by each; next, only thediffused rays of greater power returned to the antenna are kept.

This selection work reduces the number of data to be transmitted to thecentral unit 112 of the radar computer 110, and substantially withoutloss in simulation performance to the extent where the eliminateddiffused rays are rays whereof the contribution to the radar signal isvery small and therefore negligible.

According to a variant, still with the aim of limiting the quantity ofinformation raised by the RADAR propagation channel simulatoraccelerated by the GPU, the diffused rays are selected as follows:

Groups of rays having similarities in terms of position, total distancecovered by the ray, dephasing, and/or frequency are formed first. Suchcombining of rays can be done by clustering algorithms directly on thegraphics card and in parallel, by the program 114.

Each group of diffused rays is then characterized by the statisticalvalues characteristic of the group: average and variance in the totaldistance covered, average and variance of dephasing, average andvariance of the direction of reception, total power.

In this case, for selecting some of the diffused rays, the groups ofrays of greatest importance are selected. The isolated rays, or thegroups of minimal importance are assimilated with radar noise (clutter)and then eliminated.

Selection can be made by taking into account the total distance covered,optionally in addition to the criteria cited previously. For example,one can select only the N rays (N is an integer) having the shortesttotal distance covered before return to the point of reception.

Information corresponding to the groups of rays selected can thereforebe transmitted to the program 112 of the radar computer 110synthetically by transmitting only aggregated values corresponding tothe groups of selected rays.

e2) Calculations of Signals from the Diffused Rays

Data relative to the diffused rays thus selected are then transmitted tothe central unit 112 of the radar computer 110.

On reception of these information (step e2)), the program 112 calculatesa signal S_(d) for each of the selected diffused rays. This signal iscalculated on the basis of the signal initially emitted by the radar,such as shown by FIG. 7.

The respective signals S_(d) thus generated for the different selecteddiffused rays are calculated by hypothesising that the primary rays areemitted over the same time period between instants 0 and T. The durationT is selected so as to be longer as compared with the dephasing causedby the differences in flight distance between the different rays (thescales in FIGS. 7 and 8 are not representative).

Even though FIG. 7 represents a sinusoidal signal at constant frequency,it is clear that the method can be used with any type of radar signal,especially signals of variable frequencies, continuously or inincrements, for example (FSK, FMCW, . . . ).

The individual signals corresponding to each of the diffused rays have aform close to the initial radar signal, for example in the present casea sinusoidal form.

However, they are modified relative to the initial signal especially byconsidering the following parameters of the diffused ray: the phase ofthe ray, the energy or the power transported by the ray (or the powerreturned to the antenna), the polarisation of the ray, and ifappropriate the distance covered by the ray from emission of the primaryray, the frequency of the transported signal by the ray.

f) Calculation of Signal Received by Radar and of Output Signal of theRadar

Following step f), the program 112 calculates the signal S_(r) receivedby the radar by adding the respective signals S_(d) from the differentselected diffused rays, calculated at step e2).

This calculation considers reception parameters particular to the radaritself, i.e, reception antenna parameters.

On the basis of the signal S_(r) received by the radar, the program 112calculates the output signal of the radar S_(s).

The resulting output signal of the radar S_(s) is then transmitted tothe program 104 for simulating vehicle displacement (FIG. 9).

This signal S_(s) can then be subject of complementary processing, thenbe combined with other information acquired by other sensors of thevehicle, for example to feed a program automatically determining thecommands to be applied to the vehicle to ensure control or driving ofthe latter.

Finally, even though the example shown, radar having a single antennafor emission and reception has been used, the invention can beimplemented with a plurality of ray sources. It can also be implementedby evaluating the diffused rays (step d)) not for a single receptionposition, but for several reception positions.

In the example shown, the graphics card 114 constitutes both the primarycalculation means, the calculation means of diffused rays, and thecalculation means of re-emitted rays, in terms of the invention.

The invention claimed is:
 1. A computer-implemented method forgenerating an output signal outputted by a sensor for a motor vehiclewhen the sensor is placed at a point of reception facing athree-dimensional scene, the sensor being provided to emit waves andproduce the output signal as a function of waves received in returnfollowing emission of the emitted waves, the method comprising: i)simulating an emission of waves by the sensor and a propagation of thewaves so as to determine rays received by the sensor, the simulationcomprising: a) acquiring, by a processor, scene data representing thethree-dimensional scene and storing the scene data in a memory of theprocessor, wherein the scene data includes at least one object having aplurality of surfaces, each of the surfaces having a normal; b)calculating, by the processor, a plurality of primary rays to be emittedby the sensor towards the scene in respective propagation directions,each of the plurality of primary rays being defined at least by atransported power, a position, and a direction of propagation; d)calculating, by the processor, a plurality of primary diffused rays as afunction of the point of reception, each of the plurality of primarydiffused rays being emitted in a direction other than a direction of aspecular ray by a surface of the plurality of surfaces of the at leastone object of the scene reached by a primary ray of the plurality ofprimary rays; and a ray diffused by a surface reached by an incident raybeing a ray emitted by the reached surface under an effect of theincident ray, having a direction of propagation passing through thepoint of reception, and having a transported power that is at least afunction of relative orientation between the incident ray and the normalto the reached surface; and ii) determining, by the processor, theoutput signal of the sensor as a function of the rays received by thesensor and predetermined characteristics of the sensor.
 2. The methodaccording to claim 1, wherein the scene data consist mainly of at leastone multidimensional matrix or a set of individual three-dimensionaldata.
 3. The method according to claim 1, wherein when the waves areelectromagnetic, at step d) the transported power of the at least onediffused ray is calculated by using an electric field integral equation.4. The method according to claim 1, further comprising step c) wherein:c) the propagation of incident rays is simulated, especiallyiteratively, such that at each iteration for each incident ray inquestion: it is determined if the incident ray, by propagation in astraight line, reaches a surface of an object of the scene; and if as afunction of a predetermined interaction model between an incident rayand a surface of an object, at least one re-emitted ray is emitted afterthe interaction of the incident ray with the reached surface: a pointreached on the reached surface is determined; and, the at least onere-emitted ray from the reached surface is calculated; the incident raysin question being: during a first iteration, the plurality of primaryrays calculated at step b); during each subsequent iteration, there-emitted rays calculated at a preceding iteration; and at step d),diffused rays emitted by the surface of the at least one object of thescene reached by the at least one re-emitted ray are also calculated. 5.The method according to claim 4, wherein at least one property of atleast one re-emitted ray is a function of the normal of the reachedsurface.
 6. The method according to claim 4, wherein the direction ofpropagation of each of the re-emitted rays depends solely on thedirection of propagation of the incident ray and of the normal of thereached surface.
 7. The method according to claim 4, wherein when thewaves are electromagnetic, the transported power by the at least onere-emitted ray is calculated by the Snell-Descartes law.
 8. The methodaccording to claim 4, wherein step c) and/or step d) is conducted on asingle graphics card, and the calculations made for each of the rays aredone in parallel.
 9. The method according to claim 1, wherein theprimary rays, the re-emitted rays, and/or the diffused rays are recordedin a multidimensional matrix.
 10. The method according to claim 1,wherein a property of material constituting a surface of an object ofthe scene is used for calculating the re-emitted rays and/or thediffused rays.
 11. The method according to claim 1, wherein, determiningthe output signal of the sensor at step ii) comprises: e1) a sub-set ofdiffused rays is selected as a function of a predetermined criterion;e2) respective signals of the selected diffused rays are calculated onlyfor the selected sub-set of diffused rays; and f) a signal received atthe point of reception is calculated by adding the respective signalscalculated at step e2).
 12. The method according to claim 11, whereinthe predetermined criterion is a criterion taking into account thetransported power of the diffused rays, and/or at least onecharacteristic of adjacent rays.
 13. The method according to claim 12,wherein the at least one characteristic of adjacent rays is a totalcovered distance and/or a phase of a transported signal.
 14. The methodaccording to claim 1, wherein at step b) an emission diagram is providedindicating power losses as a function of the direction of propagation;and the transported power by the plurality of primary rays is calculatedas a function of the emission diagram.
 15. A computer program comprisingprogram code instructions for executing the steps of the methodaccording to claim 1 when executed on a computer.
 16. A recording mediumreadable by a computer on which a computer program comprisinginstructions for execution of steps of the method according to claim 1is recorded.
 17. The method according to claim 1, wherein the waves areelectromagnetic or acoustic waves.
 18. A wave sensor output generatorfor generating an output signal outputted by a sensor for a motorvehicle when the sensor is placed at a point of reception facing athree-dimensional scene, the sensor being provided to emit waves andproduce the output signal as a function of waves received in returnfollowing emission of the emitted waves, the sensor output generator,comprising: a processor and a memory; a) the memory, capable of storingscene data representing the three-dimensional scene including at leastone object having a plurality of surfaces, each of the plurality ofsurfaces having a normal; the processor configured to: i) simulate anemission of waves by the sensor and a propagation of the waves todetermine rays received by the sensor, comprising: b) calculating aplurality of primary rays to be emitted by the sensor towards the scenein respective propagation directions; each of the primary rays beingdefined at least by a transported power, a position, and a direction ofpropagation; d) calculating a plurality of primary diffused rays as afunction of the point of reception, each of the plurality of primarydiffused rays being emitted in a direction other than a direction of aspecular ray by a surface of the plurality of surfaces of the at leastone object of the scene reached by a primary ray of the plurality ofprimary rays; and a ray diffused by a surface reached by an incident raybeing a ray reflected by the reached surface under an effect of theincident ray, having a direction of propagation passing through thepoint of reception, and having a transported power that is at least afunction of relative orientation between the incident ray and the normalto the reached surface; and ii) determine the output signal of thesensor as a function of the rays received by the sensor andpredetermined characteristics of the sensor.
 19. The generator accordingto claim 18, further comprising c) a calculator to calculate re emittedrays at each iteration and for each incident ray in question: determinesif the incident ray, by propagation in a straight line, reaches asurface of an object of the scene; and if as a function of apredetermined interaction model between an incident ray and a surface ofan object, at least one re-emitted ray is emitted after the interactionof the incident ray with the reached surface: determines a reached pointon the reached surface; and, calculates the at least one re-emitted rayfrom the reached surface; the incident rays in question being: during afirst iteration, the plurality of primary rays calculated at step b);during each subsequent iteration, the re-emitted rays calculated at apreceding iteration; the calculator of diffused rays being furthercapable, at step d), of calculating diffused rays emitted by theplurality of surfaces of the at least one object of the scene reached bythe at least one re-emitted ray.